Acceptance Plan Basics

In general, a statistical acceptance specification is simply an acceptance procedure. An acceptance procedure is a formal procedure used to decide whether work should be accepted, rejected, or accepted at a reduced payment (Freeman and Grogan, 1998^[1]). This makes acceptance procedures a form of quality assurance. Specifically, they are monitoring methods used to determine whether or not a particular process is meeting quality standards. Acceptance procedures are not, however, a form of quality control. “Quality control” refers to a system employed to ensure the maintenance of proper quality standards within a project. Acceptance procedures simply accept or reject things or groups of things based on their quality; they do not ensure proper quality standards. Acceptance procedures should never be used as a method to control or improve quality; process controls are used to control and systematically improve quality (Montgomery, 1997^[2]). This subsection covers:

• Acceptance plan forms
• Acceptance sampling is an estimate
• Random sampling

Acceptance Plan Forms

Acceptance procedures can take one of the following three broad forms: (Montgomery, 1997^[2]):

1. Accept with no inspection is generally used when there is no economic justification to look for defective units or material.
2. 100 percent inspection is generally used where components or material are extremely critical and passing any defective components or material would result in an unacceptably high failure cost.
3. Acceptance sampling is generally used when there is some economic justification to look for defective material and either (1) some small finite percentage of defective material is acceptable or (2) it is not economical or practical to use 100 percent inspection. Acceptance sampling uses statistics to estimate information about an entire lot from a small random sample.

Of these three approaches, pavement construction typically uses acceptance sampling because excessive out-of-specification (defective) material will substantially affect long-term pavement performance but it is neither practical nor economical to inspect everything. Basically, acceptance sampling uses random sampling to make quality and material property estimates about a large amount of material. This highlights two key concepts involved in the effective use of acceptance sampling: (1) acceptance sampling only estimates material properties, and (2) acceptance sampling depends on random sampling.

Acceptance Sampling is an Estimate

Acceptance sampling uses a small number of random samples to draw conclusions about a large amount of material (called a “lot”). Since the entire lot is not inspected, these conclusions are only estimates of actual lot properties and will therefore involve some amount of uncertainty as to their accuracy. The only way to determine lot properties with certainty is to test the entire lot (100 percent inspection).

Random Sampling

Acceptance samples must be random. If samples are not random then the statistical basis for evaluating them and drawing conclusions about an entire lot is invalid. Thus, any exercise in judgment as to whether or not a sample will produce a good, failing, or average test result nullifies the random sampling assumption and therefore the assumptions on which a statistically oriented specification is based (Bowery and Hudson, 1976^[3]).

Pavement construction acceptance sampling uses a modified version of random sampling that satisfies the random sampling assumption. In true random sampling any location or item within a lot must have an equal probability of being sampled. In rare instances, this results in all samples being clustered together through random chance (Freeman and Grogan, 1998^[1]). Although this sample clustering is statistically valid, pavement specifications usually strive to ensure samples are spread more evenly throughout the lot. Therefore, stratified random sampling, which involves dividing lots into several equal-sized sublots, is generally used (Weed, 1982 as cited in Freeman and Grogan, 1998^[1]). Each individual sublot is still randomly sampled, but stratification ensures that samples are more evenly spread throughout the lot. Stratified random sampling conforms to the requirements of random sampling as long as three rules are obeyed (Weed, 1982^[4] as cited in Freeman and Grogan, 1998^[1]):

1. The same number of samples are taken from each sublot.
2. Sublots are of equal size.
3. Samples are selected randomly from within sublots.

In summary, acceptance sampling is only one of several acceptance procedure options. As such, it does not provide any direct form of quality control; it simply accepts or rejects lots. Acceptance sampling only makes estimates of actual lot properties and is dependent on random sampling to make these estimates. In order to ensure a uniform distribution of samples, the pavement construction industry typically uses stratified random sampling.